Multiply the following complex numbers: $({5-i}) \cdot ({3-3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-i}) \cdot ({3-3i}) = $ $ ({5} \cdot {3}) + ({5} \cdot {-3}i) + ({-1}i \cdot {3}) + ({-1}i \cdot {-3}i) $ Then simplify the terms: $ (15) + (-15i) + (-3i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 15 + (-15 - 3)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 15 + (-15 - 3)i - 3 $ The result is simplified: $ (15 - 3) + (-18i) = 12-18i $